Stabilization Meshless Method for Convection Dominated Problems

ZHANG Xiao-hua; OUYANG Jie; WANG Jian-yu

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2008 > 29(8): 967-975

ZHANG Xiao-hua, OUYANG Jie, WANG Jian-yu. Stabilization Meshless Method for Convection Dominated Problems[J]. Applied Mathematics and Mechanics, 2008, 29(8): 967-975.

Citation:

ZHANG Xiao-hua, OUYANG Jie, WANG Jian-yu. Stabilization Meshless Method for Convection Dominated Problems[J]. Applied Mathematics and Mechanics, 2008, 29(8): 967-975.

Citation:

ZHANG Xiao-hua, OUYANG Jie, WANG Jian-yu. Stabilization Meshless Method for Convection Dominated Problems[J]. Applied Mathematics and Mechanics, 2008, 29(8): 967-975.

PDF( 1081 KB)

Stabilization Meshless Method for Convection Dominated Problems

Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, P. R. China

Received Date: 2007-09-20
Rev Recd Date: 2008-06-26
Publish Date: 2008-08-15

Abstract

Abstract

It is well luiown that the standard Galerlan is not ideally suited to deal with the spatial discretization of convection-dominated problems.Several techniques were proposed to overcome the instability issues in convection-dominated problems simulated by meshless method.These stable techniques included: the nodal refinement,the enlazgement of nodal influence domain,the full upwind meshless technique and the adaptive upwind meshless technique.Meanwile,these stable techniques were applied to RPIM to solve one and two-dimensional convection-diffusion equations.Numerical resalts for example problems show that these techniques are effective to solve convection-dominated preblems,and the adaptive upwind meshless technique is the most effective method of all.
- meshless method,
- convection-digusion problems,
- stability methods

FullText(HTML)

References(12)

References

[1]	Donea J,Huerta A.Finite Element Methods for Flow Problems[M].Chichester:Wiley,2003.
[2]	Monaghan J J.An introduction to SPH[J].Computer Physics Communications,1988,48(1):89-96. doi: 10.1016/0010-4655(88)90026-4
[3]	Liu W K, Jun S, Zhang Y F.Reproducing kernel particle methods[J].International Journal for Numerical Methods in Fluids,1995,20(8/9):1081-1106. doi: 10.1002/fld.1650200824
[4]	Liu W K, Jun S, Sihling D T,et al.Multiresolution reproducing kernel particle method for computational fluid dynamics[J].International Journal for Numerical Methods in Fluids,1997,24(12):1391-1415. doi: 10.1002/(SICI)1097-0363(199706)24:12<1391::AID-FLD566>3.0.CO;2-2
[5]	Liu G R, Gu Y T.An Introduction to Meshfree Methods and Their Programming[M].Dordrecht: Springer,2005.
[6]	Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,1994,37(2):229-256. doi: 10.1002/nme.1620370205
[7]	Oate E, Idelsohn S, Zienkiewicz O C.A finite point method in computational mechanics: Application to convections to transport and fluid flow[J].International Journal for Numerical Methods in Engineering,1996,39(22):3839-3866. doi: 10.1002/(SICI)1097-0207(19961130)39:22<3839::AID-NME27>3.0.CO;2-R
[8]	Oate E,Idelsohn S, Zienkiewicz O C,et al.A stabilized finite point method for analysis of fluid mechanics problems[J].Computer Methods in Applied Mechanics and Engineering,1996,139(1/4):315-346. doi: 10.1016/S0045-7825(96)01088-2
[9]	Oate E,Idelsohn S.A mesh-free finite point method for advective-diffusive transport and fluid flow problems[J].Computational Mechanics,1998,21(4/5):283-292. doi: 10.1007/s004660050304
[10]	Lin H, Atluri S N. The meshless local Petrov-Galerkin (MLPG) method for convection-dynamics[J].Computer Modeling in Engineering and Sciences,2000,1(2):45-60.
[11]	张小华,欧阳洁.线性定常对流占优对流扩散问题的无网格解法[J].力学季刊,2006,27(2):220-226.
[12]	张雄, 刘岩. 无网格法[M].北京:清华大学出版社,2004.